OakCrest Academy · How it works · Physics

How a rocket reaches orbit

Reaching orbit is less a matter of going up than of going sideways: a spacecraft in low orbit travels at about 7.8 km/s parallel to the ground, so that as it falls, the curved Earth falls away beneath it at the same rate. This page follows a reusable methane-and-oxygen rocket of the kind SpaceX flies (Starship, and in many respects the smaller, kerosene-fuelled Falcon 9) through six working models, from the principle that makes any rocket move to the booster's return to the launch tower.

1Action and reaction

Newton's third law states that forces come in pairs: when one body pushes on a second, the second pushes back on the first with a force of equal size in the opposite direction. A rocket is the purest application of the law. It carries its own reaction mass (the material it throws away) and pushes that mass backward; the mass pushes the rocket forward.

A balloon on a string is a small, slow rocket. The stretched rubber keeps the air inside at about 3 kPa above room pressure (kilopascals: thousands of newtons per square meter), so air leaves the neck at roughly 71 m/s. The thrust (the forward force) equals the mass of air expelled each second multiplied by its speed.

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Model (approximate): the balloon holds about 3 kPa above room pressure, so air leaves its 1 cm neck at √(2 × 3,000 ÷ 1.2) ≈ 71 m/s with a push of about 0.47 N while the air lasts. Drag on the balloon and the straw's rubbing on the string slow it down. One, two or three pumps make a balloon about 16, 21 or 26 cm across.

Notice what is not required: something behind the balloon to push against. The balloon pushes only on its own exhaust, which is why a rocket works in the vacuum of space, and in fact works slightly better there, since no outside air presses back on the nozzle.

Explain it. Two forces of equal size act during the balloon's flight. Name the body each force acts on, and say why they do not cancel each other out. Then predict, with a reason, whether a balloon pumped three times travels further than one pumped once, and test it.

2The engine: full-flow staged combustion

A rocket engine produces the same reaction as the balloon, but with hot gas expelled at over 3 km/s. This engine burns methane (CH₄, the fuel) with oxygen (the oxidiser). Both are stored as cryogenic liquids, liquid oxygen at −183 °C and liquid methane at −162 °C, because as liquids they take up several hundred times less volume than as gases.

Two turbopumps force the liquids into the engine at very high pressure. Each pump's turbine is driven by its own small preburner: an oxygen-rich preburner burns essentially all of the oxygen with a little methane and drives the oxygen pump; a fuel-rich preburner burns essentially all of the methane with a little oxygen and drives the methane pump. After driving the turbines, both hot gas streams enter the main combustion chamber, where they finish burning at a chamber pressure of about 300 bar (300 times atmospheric pressure). Because the full flow of both propellants passes through a turbine, the cycle is called full-flow staged combustion.

The gas then accelerates through a narrowing passage to the throat, the narrowest point, where it reaches the local speed of sound (above 1 km/s in gas this hot), and expands in the bell-shaped nozzle to between two and three times that speed. A converging–diverging nozzle of this kind is a de Laval nozzle: in subsonic flow a narrowing passage speeds the gas up, but in supersonic flow the opposite holds, and a widening passage makes the gas accelerate rather than slow down.

RAPTOR 2
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CH₄ + 2 O₂ → CO₂ + 2 H₂O methane + oxygen → carbon dioxide + water vapor + heatA full-flow staged-combustion engine like SpaceX's Raptor 2 (public figures: about 300 bar in the chamber, about 230 tonnes of push at sea level, 1,630 kg, 3.6 kg of oxygen for every 1 kg of methane, throttles down to about 40 %). Both propellants pass through a preburner and a turbine before they meet in the main chamber. The tank sizes on the stand follow the real ratio: liquid oxygen is 2.7 times as dense as liquid methane, so 3.6 times the mass needs only about 1.3 times the room.

Engineers rate efficiency by specific impulse (Isp): the exhaust speed divided by standard gravity, 9.81 m/s², quoted in seconds. A methane engine at sea level achieves about 330 s, an exhaust speed of roughly 3.2 km/s; an engine with a larger nozzle optimized for vacuum reaches about 380 s. Lowering the throttle reduces propellant flow, which lowers chamber pressure and therefore thrust.

Explain it. Trace one kilogram of oxygen from the tank to the nozzle exit, naming each part it passes through and what happens to it there. Use ◀ ▶ to check your route. Then explain why it is useful that the preburners' gas is not thrown away.

3Thrust must exceed weight

Gravity pulls on the rocket with a force equal to its weight. The rocket accelerates upward only when thrust exceeds weight; the ratio of the two is the thrust-to-weight ratio, and liftoff requires it to be greater than 1. The net upward acceleration is (thrust ÷ weight − 1) × g, where g ≈ 9.81 m/s².

A fully loaded Starship stack has a mass of about 5,000 tonnes. Each of the booster's 33 engines produces about 230 tonnes-force (the force gravity exerts on 230 tonnes at the Earth's surface). Before you use the slider, calculate the smallest number of engines that will lift it.

The rocket sits on its clamps. Light some engines.

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Approximate public figures for a Super Heavy booster and Starship: about 5,000 t fully loaded, 33 Raptor engines of about 230 tonnes-force each at sea level. Heights are to scale (1 unit = 25 cm): the stack is about 123 m tall, the tower about 146 m.

5,000 ÷ 230 ≈ 21.7, so 22 engines are the minimum: 22 × 230 = 5,060 t, a thrust-to-weight ratio of 1.01 and a net acceleration of about 0.1 m/s². With all 33 engines the thrust is about 7,590 t, a ratio near 1.5. As propellant is consumed the mass falls while thrust stays nearly constant, so the acceleration increases throughout the burn.

Explain it. Explain why a rocket with a thrust-to-weight ratio of exactly 1 would hover rather than climb, and why the hold-down clamps release only after every engine is running correctly.

4The rocket equation and staging

The Russian schoolteacher Konstantin Tsiolkovsky derived, in 1897, and published, in 1903, the relation that governs every rocket:

Δv = vₑ × ln(m₀ ÷ mf)

Δv (delta-v) is the change in velocity the rocket can produce; vₑ is the exhaust velocity; m₀ is the initial mass, fully fueled; mf is the final mass once the propellant is spent. The quotient m₀ ÷ mf is the mass ratio, and ln is the natural logarithm, which grows ever more slowly: doubling the mass ratio adds only vₑ × ln 2 ≈ 0.69 vₑ, whatever the starting point. Every additional tonne of propellant must also be carried, so the returns diminish.

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Model numbers (rounded, approximate): exhaust speed vₑ = 3.5 km/s; 4,600 t of propellant, 300 t of tanks and engines and 100 t of payload in both versions. One stage: m₀ ÷ m_f = 5,000 ÷ 400 = 12.5, Δv = 3.5 × ln 12.5 ≈ 8.8 km/s. Two stages (3,400 t + 200 t booster, 1,200 t + 100 t ship): 3.5 × ln(5,000 ÷ 1,600) + 3.5 × ln(1,400 ÷ 200) ≈ 4.0 + 6.8 = 10.8 km/s. Orbit needs about 9.4.

Low orbit requires about 9.4 km/s of Δv: 7.8 km/s of orbital speed plus roughly 1.6 km/s lost to gravity and air resistance during the climb. A single stage carrying 92 % propellant reaches only about 8.8 km/s. Divide the same propellant and the same structure into two stages, discard the empty booster, and the second stage starts its burn without 200 t of empty tanks and engines; the total rises to about 10.8 km/s. That margin is what pays for carrying propellant back for the booster's landing.

Explain it. Without numbers, explain why discarding the empty booster increases the final speed even though no extra propellant has been added. Then calculate the Δv of a stage with a mass ratio of 3 and vₑ = 3.5 km/s (ln 3 ≈ 1.10).

5The climb to orbit

An orbit is a state of continuous free fall. At 200 km altitude gravity is still about 94 % as strong as at the surface; a spacecraft stays up only because its horizontal speed, about 7.8 km/s, carries it far enough sideways in each second that the Earth's curved surface drops away by exactly as much as the craft falls. Isaac Newton described this with an imaginary cannon on a mountaintop firing ever faster cannonballs.

The rocket therefore rises vertically for only a few seconds, to clear the tower, then pitches over slightly and allows gravity to bend its path progressively toward the horizontal. This gravity turn keeps the rocket's nose aligned with its direction of travel, minimizing sideways aerodynamic loads.

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A typical climb to a low orbit of about 190 km (rounded; every flight differs): Max-Q about 62 s after liftoff near 11 km, main-engine cut-off and separation at about 2½ minutes near 66–69 km and 1.5 km/s, orbit at about 8 min 50 s and 7.8 km/s, about 1,600 km downrange. Heights above the ground are stretched 10×, the crust is drawn 4× thicker, and the rocket is drawn far larger than true scale; distances along the ground are true.

Max-Q is the moment of maximum dynamic pressure (q = ½ρv², where ρ is air density and v speed): the rocket is fast, but the air is still dense, so aerodynamic stress peaks, about a minute after liftoff. MECO (main-engine cut-off) ends the booster's burn; the stages separate; and the second stage continues until it reaches orbital velocity, a moment called orbit insertion.

Explain it. Use the Up and Sideways bars to describe how the rocket's effort shifts during the flight. Then explain, in terms of falling and the Earth's curvature, why a spacecraft at 7.8 km/s does not come down.

6Returning the booster

Expendable boosters were discarded after a single flight. A reusable booster returns to be refuelled and flown again, which reduces the cost of each launch dramatically, at the price of carrying extra propellant and hardware for the return.

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Approximate sequence for a Super Heavy booster (rounded, varies by flight): separation at about 65 km and 1.5 km/s; flip within about 10 s; boostback burn of about 50 s; a coast of a few minutes with grid fins steering; a landing burn in the last kilometer or two, on 13 engines then 3; caught roughly 6 to 7 minutes after liftoff. The booster, arms and tower are drawn to the same scale; the path through the sky is squeezed to fit (in reality it reaches tens of kilometers out).

After separation the booster flips to point its engines along its direction of travel, then fires a boostback burn to cancel its outward velocity and reverse toward the launch site. It falls tail-first, steered by grid fins (lattice control surfaces that remain effective at supersonic speed), and immediately before arrival lights its engines for the landing burn, decelerating from hundreds of kilometers per hour to nearly zero.

Falcon 9 boosters, which burn kerosene and liquid oxygen, add an entry burn to slow down before the densest air and touch down on four unfolding landing legs, on land or on a drone ship at sea. Super Heavy carries no legs at all: the launch tower's arms catch it by two pins, saving the mass that legs would have cost on every flight.

Explain it. Put the six phases of the return in order and give the purpose of each in one sentence. Then argue one advantage and one disadvantage of catching a booster with a tower instead of landing it on legs.